Lastly, Monte Carlo Dropout (MCDropout) applies Dropout at inference time allows for computationally efficient UE.
[1]}
show that Dropout [2]}
approximates Bayesian inference of a GP.
Given \(M\)  models \(\lbrace \mathcal {C}_{{\mathbf {\omega }}}^{m}\rbrace _{m=1}^M\)  sampled with MC Dropout, where each outputs non-scaled values—“logits”, we define \(\hat{{\mathbf {y}}} \in \mathbb {R}^C\)  as the average prediction:
\(\hat{{\mathbf {y}}} \! = \! \frac{1}{M} \smash{\sum _{m=1}^M} \mathop {\rm Softmax}\big (\mathcal {C}^{m}_{\mathbf {\omega }}({\mathbf {x}})\big ).\) 
Given \(\hat{{\mathbf {y}}}\) , there are several ways to estimate the model's uncertainty, see [3]}.
We use the entropy of the output distribution (over the classes) to quantify the uncertainty estimate of a given sample \({\mathbf {x}}\) :
\(\mathcal {H}({\mathbf {x}}, {\mathbf {\omega }})\! =\! - \sum _{c \in C} \hat{{\mathbf {y}}}_c \log \hat{{\mathbf {y}}}_c \,.\)
